Calculate the yield to maturity on the following bonds: a. A 9.2 percent coupon

Question

Calculate the yield to maturity on the following bonds:

a. A 9.2 percent coupon (paid semiannually) bond, with a $1,000 face value and 17 years remaining to maturity. The bond is selling at $975.

b. An 8.2 percent coupon (paid quarterly) bond, with a $1,000 face value and 10 years remaining to maturity. The bond is selling at $905.

c. An 11.2 percent coupon (paid annually) bond, with a $1,000 face value and 6 years remaining to maturity. The bond is selling at $1,055. (For all requirements, do not round intermediate calculations. Round your answers to 3 decimal places. (e.g., 32.161))

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Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of $1,000, have 10 years remaining to maturity, and have a required rate of return of 12 percent

a. The bond has a 5.8 percent coupon rate. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

b. The bond has a 7.8 percent coupon rate. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

c. The bond has a 12 percent coupon rate. (Do not round intermediate calculations.)

Explanation / Answer

Answer to Question 1:

Answer a.

Face Value = $1,000
Current Price = $975

Annual Coupon Rate = 9.2%
Semiannual Coupon Rate = 4.60%
Semiannual Coupon = 4.60%*$1,000 = $46

Time to Maturity = 17 years
Semiannual Period to Maturity = 34

Let semiannual YTM be i%

$975 = $46 * PVIFA(i%, 34) + $1,000 * PVIF(i%, 34)

Using financial calculator:
N = 34
PV = -975
PMT = 46
FV = 1000

I = 4.75%

Semiannual YTM = 4.75%
Annual YTM = 2 * 4.75%
Annual YTM = 9.50%

Answer b.

Face Value = $1,000
Current Price = $905

Annual Coupon Rate = 8.2%
Quarterly Coupon Rate = 2.05%
Quarterly Coupon = 2.05%*$1,000 = $20.50

Time to Maturity = 10 years
Period to Maturity = 40 quarters

Let Quarterly YTM be i%

$905 = $20.50 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -905
PMT = 20.50
FV = 1000

I = 2.42%

Quarterly YTM = 2.42%
Annual YTM = 4 * 2.42%
Annual YTM = 9.68%

Answer c.

Face Value = $1,000
Current Price = $1,055

Annual Coupon Rate = 11.20%
Annual Coupon = 11.20%*$1,000 = $112

Time to Maturity = 6 years

Let Annual YTM be i%

$1,055 = $112 * PVIFA(i%, 6) + $1,000 * PVIF(i%, 6)

Using financial calculator:
N = 6
PV = -1,055
PMT = 112
FV = 1000

I = 9.94%

Annual YTM = 9.94%

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